An
escalator can never break: it can only become stairs. You should
never see an "Escalator Temporarily Out Of Order" sign,
just "Escalator Temporarily Stairs. Sorry for the convenience"
- Mitch Hedberg

Some
things in life are bad,
They can really make you mad,
Other things just make you swear and curse,
When you're chewing life's gristle,
Don't grumble,
Give a whistle
And this'll help things turn out for the best.
And...

Always
look on the bright side of life.
[whistle]
Always look on the light side of life.
[whistle]

If
life seems jolly rotten,
There's something you've forgotten,
And that's to laugh and smile and dance and sing.
When you're feeling in the dumps,
Don't be silly chumps.
Just purse your lips and whistle.
That's the thing.
And...

Always
look on the bright side of life.
[whistle]
Always look on the right side of life,
[whistle]

For
life is quite absurd
And death's the final word.
You must always face the curtain with a bow.
Forget about your sin.
Give the audience a grin.
Enjoy it. It's your last chance, anyhow.
So,...

Always
look on the bright side of death,
[whistle]
Just before you draw your terminal breath.
[whistle]

Life's
a piece of ****,
When you look at it.
Life's a laugh and death's a joke it's true.
You'll see it's all a show.
Keep 'em laughing as you go.
Just remember that the last laugh is on you.
And...

Always
look on the bright side of life.
Always look on the right side of life.
[whistle]
Always look on the bright side of life!
[whistle]
Always look on the bright side of life!
[whistle]
Always look on the bright side of life!
[whistle]
Repeat to fade...

Previous
Puzzles of the Month + Solutions

The
Geometry of the Bees...The
shape of the wax
cells is such that two opposing honeycomb layers nest into each other, with
each facet of the closed ends being shared by opposing cells, and with the open
ends facing outward, as illustrated in fig. 1 above. Each cell is actually a
rhombic decahedron, that is an hexagonal prism having three rhombi at its closed
end (as shown in fig. 2 above). In short, each cell is a ten-sided structure
with one side open. Mathematicians made extensive studies of the isoperimetric
properties of the honeycomb cells and believed them to be the most efficient
design possible. If the faces of every cell contain the LARGEST possible volume
with the LEAST possible surface, what is the value of the angle alpha?
The faces of the hexagonal prism are each 1-unit wide...

b)
The diagonal AB of the rhombus at the
closed end of the cell does not depend upon its
spatial angulation (the axis AB remains
the same even when the spatial angle changes, fig.
4) but upon the sides of the hexagonal prism and
the radius r that circumscribes the hexagonal
section. Thus the length of AB is:
2√[12 - (1/2)2] = √(4
- 4/4) = √3

c)
So, the area of each of the 3 rhombi at the closed
end of the cell is:dl/2
or
√3 √(4x2 + 1)/2

Curiously,
a 3-dimensional honeycomb partition is not optimal!
In 1965, the Hungarian mathematician László Fejes
Tóth discovered that a cell end composed
of two hexagons and two smaller rhombi (see fig.
opposite), instead of three rhombi, would actually
be 0.035% (or approximately 1 part per 2850) more
efficient. But, frankly, this difference is too minute
to measure on an actual honeycomb, and irrelevant
to the hive economy in terms of efficient use of
wax, and because the honeycomb walls have a definite
thickness, it is not clear that Tóth's structure
would indeed be an improvement... In that respect,
the honeycomb is more like a wet foam than a dry
foam. Several years ago, the physicist D.
Weaire and his colleague R. Phelan undertook
to construct two-layer foams with equal-sized bubbles,
and they found that the dry foams did take on Tóth's
pattern. But when they gradually added liquid to
thicken the bubble walls, something 'quite dramatic'
happened: the structure suddenly switched over to
the three-rhombus configuration of a honeycomb (it
seems, then, that the bees got it right after all!).
The switch also occurs in the reverse direction as
liquid is removed.